## Search

Now showing items 1-7 of 7

#### Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case

(SIAM, 2009)

In this paper, we review two types of doubling algorithm and some
techniques for analyzing them.
We then use the techniques to study the doubling algorithm for three
different nonlinear matrix equations in the critical ...

#### Solving a structured quadratic eigenvalue problem by a structure-preserving doubling algorithm

(SIAM, 2010)

In studying the vibration of fast trains, we encounter a palindromic quadratic eigenvalue problem (QEP) $(\lambda^2 A^T + \lambda Q + A)z = 0$, where $A, Q \in \mathbb{C}^{n \times n}$ and $Q^T = Q$. Moreover, the matrix ...

#### Numerical solution of nonlinear matrix equations arising from Green's function calculations in nano research

(Elsevier, 2012)

The Green's function approach for treating quantum transport in nano devices requires the solution of nonlinear matrix equations of the form
$X+(C^*+{\rm i} \eta D^*)X^{-1}(C+{\rm i} \eta D)=R+{\rm i}\eta P$, where $R$ ...

#### Convergence rates of some iterative methods for nonsymmetric algebraic Riccati equations arising in transport theory

(Elsevier, 2010)

We determine and compare the convergence rates of various
fixed-point iterations for finding the minimal positive solution of
a class of nonsymmetric algebraic
Riccati equations arising
in transport theory.

#### Complex symmetric stabilizing solution of the matrix equation $X+A^{T}X^{-1}A=Q$

(Elsevier, 2011)

We study the matrix equation $X+A^{T}X^{-1}A=Q$, where $A$ is a complex square matrix and $Q$ is complex symmetric.
Special cases of this equation appear in Green's function calculation in nano research and also in
the ...

#### On a nonlinear matrix equation arising in nano research

(SIAM, 2012)

The matrix equation $X+A^{T}X^{-1}A=Q$ arises in Green's function calculations in nano
research, where $A$ is a real square matrix and $Q$ is a real symmetric matrix dependent on a parameter
and is usually indefinite. ...

#### The matrix equation $X+A^TX^{-1}A=Q$ and its application in nano research

(SIAM, 2010)

The matrix equation $X+A^TX^{-1}A=Q$ has been studied extensively when $A$
and $Q$ are real square matrices
and $Q$ is symmetric positive definite. The equation has positive definite
solutions under suitable conditions, ...